If 180°<θ<270°, and sinθ=−3/4, what is the value of sin(−θ)?
1 answer:
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Answer:
The simplified form is .
is the excluded value for the given expression.
Step-by-step explanation:
Given:
The expression given is:
Let us simplify the numerator and denominator separately.
The numerator is given as
2 is a common factor in all the three terms. So, we factor it out. This gives,
Now,
Therefore, the numerator becomes
The denominator is given as:
Factoring out 3, we get
Now, is of the form
So,
Therefore, the denominator becomes
Now, the given expression is simplified to:
There is in the numerator and denominator. We can cancel them only if
as for
, the given expression is undefined.
Now, cancelling the like terms considering , we get:
Therefore, the simplified form is
The simplification is true only if . So,
is the excluded value for the given expression.